Ricardo Quaresma smashed home an early penalty after Manuel Neuer was lucky not to be sent off for felling Jackson Martinez.
And Quaresma stunned the German champions when he plundered Dante in defence before slotting under Neuer to double Porto's lead.
Bayern, missing Arjen Robben, Franck Ribery and a number of other key players, hit back through a Thiago Alcantara tap-in mid-way through the first half.
But Jackson Martinez restored the home side's two-goal lead when he latched on to a long ball and rounded the goalkeeper before prodding home.
The result leaves Bayern's hopes of qualifying for a fifth straight semi-final hanging in the balance, with the two sides set to meet for the second leg in two week's time in Munich.